## Preliminary list of abstracts

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Observations on alternating least squares
Mon, 14:25--14:50
• Mohlenkamp, Martin (Mathematics, Ohio University, United States)

Approximating a multidimensional object by a sum of separable objects is an effective way to bypass the curse of dimensionality. The simplest, most robust, and most common algorithm to do so is Alternating Least Squares (ALS). We observe that ALS can be viewed as alternately setting partial gradients to zero or as alternately performing orthogonal projections. These dual perspectives allow us to analyze the convergence of ALS. For example, we can show that the $L^2$ norms of the increments form a sequence in $l^2$, but may not be in $l^1$. When regularization is included, we can show for example that the gradient is zero at all accumulation points.